球型机器人状态方程直接积分解法

doi:10.3969/j.issn.0372-2112.2016.12.029

电子学报 ›› 2016, Vol. 44 ›› Issue (12): 3020-3025.DOI: 10.3969/j.issn.0372-2112.2016.12.029

球型机器人状态方程直接积分解法

曹少中, 赵伟

北京印刷学院高端印刷装备信号与信息处理北京市重点实验室, 北京 102600

收稿日期:2015-12-07 修回日期:2016-03-13 出版日期:2016-12-25
- 作者简介:
- 曹少中,男,1965年2月生于河北保定,博士,2005年毕业于北京理工大学信息工程学院,现为北京印刷学院信息工程学院教授.主要研究方向为非线性系统理论,机器人控制理论.E-mail:caoshaozhong@bigc.edu.cn;赵伟,男,1983年9月出生,山东泰安人,博士,2015年于北京邮电大学自动化学院获得工学博士学位.现为北京印刷学院信息工程学院讲师.主要研究方向为机器人技术.E-mail:zhaoweihu@163.com
- 基金资助:
- 国家自然科学基金 (No.61272030，No.61472461）

Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Spherical Robot

CAO Shao-zhong, ZHAO Wei

Beijing Key Laboratory of Signal and Information Processing for High-end Printing Equipment, Beijing Institute of Graphic Communication, Beijing 102600, China

Received:2015-12-07 Revised:2016-03-13 Online:2016-12-25 Published:2016-12-25

摘要/Abstract

摘要：

非线性系统分析的核心归结为系统状态方程的求解问题，对于一般非线性控制系统，通过引入由状态量、控制量与自变量时间坐标构成的“广义状态空间”，在广义状态空间一点将方程的右端展开为时间的Taylor级数，进一步直接积分获得非线性控制系统状态方程关于自变量时间的级数解.以球型机器人这种存在耦合的非线性系统为例，设计一种自适应滑模控制器，利用本文提出的解法得出了控制量与输出量的解析解，并仿真验证了方法的正确性.

关键词: 球型机器人, 滑膜控制, 非线性控制系统, 状态方程, 直接积分

Abstract:

The kernel of nonlinear system analysis is the solving of system state equation.Therefore,for a general nonlinear control system,the concept of general time-state space comprising of state variables,control variable,and time t is introduced.In order to solve the state equation of nonlinear control systems,at the operation point of general time-state space,the right side of the state equation can be expanded as Taylor series about time.Then the series solution of the nonlinear control state equation,for which the solution is expressed in time series,can be obtained by using direct-integrating approach.Sliding mode controller is established to control the typical coupling nonlinear system model of the spherical robot.Then we obtain the analytical solution of control and controlled variable by the direct-integrating method.The validity of this method is verified by experiment.

Key words: spherical robot, sliding mode control, nonlinear control systems, state equation, direct-integrating

中图分类号:

TP273

曹少中, 赵伟. 球型机器人状态方程直接积分解法[J]. 电子学报, 2016, 44(12): 3020-3025.

CAO Shao-zhong, ZHAO Wei. Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Spherical Robot[J]. Acta Electronica Sinica, 2016, 44(12): 3020-3025.

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球型机器人状态方程直接积分解法

Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Spherical Robot

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